Question Number 34063 by rahul 19 last updated on 30/Apr/18 $$\boldsymbol{\mathrm{L}}\mathrm{et}\:\mathrm{A}=\:\left\{\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\right\}\:.\:\mathrm{N}{umber}\:\mathrm{of}\:\mathrm{functions} \\ $$$$\mathrm{f}:\mathrm{A}\rightarrow{A}\:\mathrm{satisfying}\:\mathrm{f}\left(\mathrm{f}\left({x}\right)\right)={x}\:\forall{x}\in\mathrm{A},\:\mathrm{is}\:? \\ $$ Commented by rahul 19 last updated on 30/Apr/18 $${Ans}.\:{is}\:\mathrm{13}…. \\…
Question Number 99580 by mathmax by abdo last updated on 21/Jun/20 $$\mathrm{let}\:\mathrm{A}\:=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{A}\:\mathrm{is}\:\mathrm{inversible}\:\mathrm{and}\:\mathrm{calculste}\:\mathrm{A}^{−\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{e}^{\mathrm{A}} \:\mathrm{and}\:\mathrm{e}^{−\mathrm{A}} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{calculate}\:\mathrm{cos}\:\mathrm{A}\:\mathrm{and}\:\mathrm{sinA}\:\:\:\mathrm{is}\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{A}\:+\mathrm{sin}^{\mathrm{2}} \:\mathrm{A}\:=\:\mathrm{I}\:? \\ $$$$…
Question Number 34029 by rahul 19 last updated on 29/Apr/18 $$\boldsymbol{{N}}{umber}\:{of}\:{integral}\:{values}\:{of}\:{x}\:{for} \\ $$$${which}\: \\ $$$$\frac{\left(\frac{\pi}{\mathrm{2}^{\mathrm{tan}^{−\mathrm{1}} {x}} }−\mathrm{4}\right)\left({x}−\mathrm{4}\right)\left({x}−\mathrm{10}\right)}{{x}!\:−\:\left({x}−\mathrm{1}\right)!}\:<\:\mathrm{0} \\ $$ Commented by rahul 19 last updated…
Question Number 34013 by math khazana by abdo last updated on 29/Apr/18 $${find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left(\left(\mathrm{2}{n}+\mathrm{1}\right)\frac{\pi}{\mathrm{4}}\right)}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34011 by math khazana by abdo last updated on 29/Apr/18 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{{n}^{\mathrm{2}} }\:\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{2}} } \\ $$ Terms of Service Privacy…
Question Number 33997 by rahul 19 last updated on 29/Apr/18 $$\boldsymbol{{I}}\mathrm{f}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left({x}\right)\:=\:\frac{{x}−\mathrm{1}}{\mathrm{p}−{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{does}\:\mathrm{not}\:\mathrm{contain}\:\mathrm{any} \\ $$$$\mathrm{values}\:\mathrm{belonging}\:\mathrm{to}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left[−\mathrm{1},\frac{−\mathrm{1}}{\mathrm{3}}\right]\:{then}\:{true}\:{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{p}\:\mathrm{is}\:? \\ $$ Answered by ajfour last updated…
Question Number 33990 by abdo imad last updated on 28/Apr/18 $${let}\:{give}\:{I}\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right){dx}\: \\ $$$${give}\:{I}\:{at}\:{form}\:{of}\:{serie}\:. \\ $$ Commented by abdo imad last updated on 01/May/18…
Question Number 33985 by abdo imad last updated on 28/Apr/18 $${prove}\:{that}\:\frac{\mathrm{1}}{\mathrm{1}+{cosx}}\:=\mathrm{2}\sum_{{n}=\mathrm{1}} ^{\infty} {n}\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {cos}\left({nx}\right)\:{for} \\ $$$${x}\neq{k}\pi\:,{k}\in\:{Z}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33981 by abdo imad last updated on 28/Apr/18 $${let}\:{x}\in\left[−\mathrm{1},\mathrm{1}\right]\:{andf}_{{n}} \left({x}\right)={sin}\left(\mathrm{2}{narcsinx}\right) \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:{f}_{{n}} {is}\:{odd}\:{and}\:{calculate}\:{f}_{{n}} \left(\mathrm{0}\right)\:{and}\:{f}_{{n}} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right){solve}\:{inside}\:\left[\bar {\mathrm{0}1}\right]\:\:{f}_{{n}} \left({x}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:{f}_{{n}} \:{is}\:{continue},{derivable}\:{on}\left[−\mathrm{1},\mathrm{1}\right]\:{and} \\…
Question Number 33944 by rahul 19 last updated on 28/Apr/18 $$\boldsymbol{\mathrm{I}}\mathrm{f}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\left(\mathrm{p}^{\mathrm{2}} −\mathrm{4}\right)\left(\mathrm{p}^{\mathrm{2}} −\mathrm{9}\right){x}^{\mathrm{3}} +\left[\frac{\mathrm{p}−\mathrm{2}}{\mathrm{2}}\right]{x}^{\mathrm{2}} +\left(\mathrm{p}−\mathrm{4}\right)\left(\mathrm{p}−\mathrm{3}\right)\left(\mathrm{p}−\mathrm{2}\right){x}+\left\{\mathrm{2p}−\mathrm{1}\right\}=\mathrm{0}. \\ $$$$\mathrm{is}\:\mathrm{satisfied}\:\mathrm{by}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{in}\:\left(\mathrm{0},\mathrm{3}\right]\:{then} \\ $$$${sum}\:{of}\:{all}\:{possible}\:{integral}\:{values}\:{of} \\ $$$$'{p}'\:{is}\:? \\ $$$$\left\{.\right\}\:=\:{fractional}\:{part}\:{function}.…